I am puzzled by some methods for gradient reconstruction in literature. For Gauss based method, two general methods can be found. The first one is given by Ferziger and Peric's book, gradient is calculated by a iterative method based on gradient(p)= sum[(0.5*(p1+p2)+gradient(p)*x)*sx/v]. The second one can be found in the online-help of STar-CCM+

In the second one, a limiter is introduced. According to S. R. Mathur and Murthy (1997), A PRESSURE-BASED METHOD FOR UNSTRUCTURED MESHES, heat transfer, The formula is likely expressed as gradient(p)=sum (0.5*(p1+p2)*sx/v*limiter).

My questions are

(1) my understanding of the second one is correct or not? iterative calculations are not necessary if limiter is there, right?

(2) the first one could exceed the maximum and minimum of the neighboring cell centroid values, right?